1. Technical Field
The present invention generally relates to designing low-density parity-check codes (LDPC) and, more specifically, to methods and systems for constructing base matrices of quasi-cyclic (QC)-LDPC.
2. Description of the Related Art
Several different design methods for constructing QC-LDPC codes have been explored and studied. In particular, many of such methods employ algebraic and combinatorial technologies. The design criterion of the algebraic construction is to increase the minimum distance, i.e., dmin, which can correspond to, for example, the Hamming distance of the codeword set. Using these methods, different code block lengths can be obtained by changing the size of cyclic submatrices based on algebraic properties. Other types of QC-LDPC design methods include pseudo-random LDPC construction approaches, which utilize certain code graph metrics to design the QC-LDPC code for iterative decoding.
For example, in one approach, the QC-LDPC codes are constructed using a progressive edge growth (PEG) technique. Here, a base matrix structure and a single targeted lifting size are used to construct a base matrix for QC-LPDC with the targeted lifting size such that the lower bound of the codeword error probability (WER) is minimized. The design criterion is to construct QC-LDPC codes that provide a minimized block error probability (BEP) or BEP upper bound in Binary Erasure Channels (BEC), which is formulated based on the e-cycle. Specifically, e-cycles are searched to evaluate the lower bound of the WER. The design is configured for a particular lifting size L.